PRE-IMAGE ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS*

The authors define and study topological pre-image entropy for the non-autonomous discrete dynamical systems given by a sequence {fi}i=1^∞ of continuous self-maps of a compact topological space. The basic properties and the invariant with respect to equiconjugacy of pre-image entropy for the non-autonomous discrete dynamical systems are obtained.     

The projective plane crossing numbers of circular graphs*

The authors give an upper bound for the projective plane crossing number of a circular graph. Also, the authors prove the projective plane crossing numbers of circular graph C （8, 3） and C （9, 3） are 2 and 1, respectively.     

Asymptotic Solution of Activator Inhibitor Systems for Nonlinear Reaction Diffusion Equations

A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.     

HEAVY TRAFFIC LIMIT THEOREMS IN FLUID BUFFER MODELS

A fluid buffer model with Markov modulated input-output rates is considered.When traffic intensity is near its critical value, the system is known as in heavy traffic.It is shown that a suitably scaled sequence of the equilibrium buffer contents has a weakor distributional limit under heavy traffic conditions. This weak limit is a functional of adiffusion process determined by the Markov chain modulating the input and output rates.The first passage time of the reflected process is examined. It is shown that the mean firstpassage time can be obtained via a solution of a Dirichlet problem. Then the transitiondensity of the reflected process is derived by solving the Kolmogorov forward equation witha Neumann boundary condition. Furthermore, when the fast changing part of the generatorof the Markov chain is a constant matrix, the representation of the probability distributionof the reflected process is derived. Upper and lower bounds of the probability distributionare also obtained by means of asymptotic e     

A Priority-Based Negotiations Approach for Handling Inconsistencies in Multi-Perspective Software Requirements

Inconsistency of multi-perspective requirements specifications is a pervasive issue during the requirements process. However, managing inconsistency is not just a pure technical problem. It is always associated with a process of interactions and competitions among corresponding stakeholders. The main contribution of this paper is to present a negotiations approach to handling inconsistencies in multi-perspective software requirements. In particular, the priority of requirements relative to each perspective plays an important role in proceeding negotiation over resolving inconsistencies among different stakeholders. An algorithm of generating negotiation proposals and an approach to evaluating proposals are also presented in this paper, respectively.     

A STAGE-STRUCTURED SI ECO-EPIDEMIOLOGICAL MODEL WITH TIME DELAY AND IMPULSIVE CONTROLLING*

This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of the ＇pest-eradication＇ periodic solution and permanence of the system depend on time delay, hence, the authors call it ＂profitless＂. Further, the authors present a pest management strategy in which the pest population is kept under the economic threshold level （ETL） when the pest population is uniformly persistent. By numerical analysis, the authors also show that constant maturation time delay for the susceptible pests and pulse releasing of the infectious pests can bring obvious effects on the dynamics of system.     

A modified likelihood ratio test for homogeneity in bivariate normal mixtures of two samples

This paper investigates the asymptotic properties of a modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models of two samples. The asymptotic null distribution of the modified likelihood ratio statistic is found to be χ₂², where χ₂² is a chi-squared distribution with 2 degrees of freedom. This research was supported by the National Natural Science Foundation of China under Grant No. 10661003, SRF for ROCS, SEM under Grant No. [2004]527, and the Natural Science Foundation of Guangxi under Grant No. 0728092.     

RELAXED CONDITIONS FOR CONSENSUS IN MULTI-AGENT COORDINATION

This paper proposes relaxed sufficient conditions for the consensus of multi-agent systems by the averaging protocols with time-varying system topology. Bidirectional information exchange between neighboring agents is considered and both the discrete-time and continuous-time consensus protocols are studied. It is shown that the consensus is reached if there exists an unbounded time sequence such that two agents who own the maximum and minimum states at each time instant in the sequence will be jointly connected at some future time. Further, this result is applied to the original nonlinear Vicsek model, and a sufficient condition for the heading consensus of the group with restricted initial conditions is obtained.     

CONVERGENCE PROPERTIES OF THE DEPENDENT PRP CONJUGATE GRADIENT METHODS

In this paper, a new region of βk with respect to ;βk^PRP is given. With two Armijo-type line searches, the authors investigate the global convergence properties of the dependent PRP conjugate gradient methods, which extend the global convergence results of PRP conjugate gradient method proved by Grippo and Lucidi （1997） and Dai and Yuan （2002）.     

ON APPROXIMATION BY REPRODUCING KERNEL SPACES IN WEIGHTED L^p SPACES

In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.     

ON CHARACTERIZATIONS OF D-η-PROPERLY PREQUASI-INVEX FUNCTION

Recently, various concepts of D-η-properly prequasi-invex functions were introduced and characterizations of D-η-properly prequasi-invex functions were presented under a certain set of conditions. In this paper, we show that the same results can be obtained under weaker assumptions.     

Estimation on semivarying coefficient models with different degrees of smoothness

Semivarying coefficient models are frequently used in statistical models. In this paper, under the condition that the coefficient functions possess different degrees of smoothness, a two-step method is proposed. In the case, one-step method for the smoother coefficient functions cannot be optimal. This drawback can be repaired by using the two-step estimation procedure. The asymptotic mean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate of convergence. A few simulation studies are conducted to evaluate the proposed estimation methods. This research is supported in part by the National Natural Science Foundation of China under Grant No. 10871072 and Shanxi's Natural Science Foundation of China under Grant No. 2007011014.     

STUDIES ON HORIZONTAL COMPETITION AMONG HOMOGENOUS RETAILERS THROUGH AGENT-BASED SIMULATION

1. Introduction A supply chain is a network composed osuppliers, manufacturers, retailers, etc., whichcooperate to offer a kind of goods or servicesThese supply chain members cooperate andcompete with each other to maximize theiown profits. For example,…     

OPTIMAL BIRTH CONTROL FOR AN AGE-DEPENDENT COMPETITION SYSTEM OF N SPECIES

In this paper, we investigate optimal policies for an age-dependent n-dimensional competition system, which is controlled by fertility. By using Dubovitskii-Milyutin＇s general theory, the maximum principles are obtained for the problems with free terminal states, infinite horizon, and target sets, respectively.     

SUPERCONVERGENCE ANALYSIS OF A NONCONFORMING TRIANGULAR ELEMENT ON ANISOTROPIC MESHES

The class of anisotropic meshes we conceived abandons the regular assumption. Some distinct properties of Carey＇s element are used to deal with the superconvergence for a class of two- dimensional second-order elliptic boundary value problems on anisotropic meshes. The optimal results are obtained and numerical examples are given to confirm our theoretical analysis.     

STABILITY ANALYSIS OF TWO-SECTORS STOCHASTIC ECONOMIC GROWTH MODEL

In the paper, we investigate the stability of a two-sector economic growth model under stochastic case. A two-dimensional stochastic differential system is deduced by Ito＇s formula, by using Lyapunov function methods, whether the growth rates of physical capital and human capital are exponentially stable or unstable depends on the values for parameters. Finally, we also illustrate the results with two examples.     

MINIMAX INVARIANT ESTIMATOR OF CONTINUOUS DISTRIBUTION FUNCTION UNDER LINEX LOSS

In this paper we consider the problem of estimation of a continuous distribution function under the LINEX loss function. The best invariant estimator is obtained and proved to be minimax for any sample size n ≥ 1.     

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS II： M（n）/G/1/K

We study a single-server queueing system with state-dependent arrivals and general service distribution, or simply M（n）/G/1/K, where the server follows an N policy and takes multiple vacations when the system is empty. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirements are the Laplace-Stieltjes transforms of the service time distribution and the vacation time distribution, and the state-dependent arrival rate. The computational complexity of the algorithm is O（K^3）.     

Asymptotic Normality of Maximum Quasi-Likelihood Estimators in Generalized Linear Models with Fixed Design*

In generalized linear models with fixed design, under the assumption λ↑_n→∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator ^↑βn, which is the root of the quasi-likelihood equation with natural link function ∑i=1^n Xi（yi -μ（Xi′β）） = 0, is obtained, where λ↑_n denotes the minimum eigenvalue of ∑i=1^nXiXi′, Xi are bounded p × q regressors, and yi are q × 1 responses.     

Technical Note ：SINGLE-PERIOD TWO-PRODUCT INVENTORY MODEL WITH SUBSTITUTION： SOLUTION AND PROPERTIES

In this paper, we study a single-period two-product inventory model with stochastic demands and downward substitution. The optimal order quantities are presented and some properties are provided. Comparing with newsboy model, we prove that both the profit and the fill rate can be improved by using the substitution policy. This work was supported partly by NSFC/RGC Joint Research Program under grant 79910161987 and the National Science Foundation of China (79825102, 70231010, 70321001). Lianqiao CAI is lecturer of School of International Business, Beijing Foreign Studies University. He received his B.S. and M.S. from School of Economics and Management, Tsinghua University, in 1995 and 1998, and Ph.D of Management Science from Tsinghua University in 2002. His research areas include supply chain management, optimization techniques. Jian Chen is Professor and Chairman of the Management Science Department and co-director of the Research Center for Contemporary Management, Tsinghua University. He has over 80 papers published in some leading international journals and first class Chinese journals, and has been a principal investigator for over 20 grants or research contracts with National Science Foundation of China, governmental organizations, and companies. His main research interests include supply chain management, E-commerce, modeling and control for complex systems, decision support systems and information systems, and forecast and optimization techniques. He serves as associate editor of the “IEEE Transactions on Systems, Man and Cybernetics: Part A” and “IEEE Transactions on Systems, Man and Cybernetics: Part C”, and on the Editorial Board of “The International Journal of Electronic Business” and “System Research and Behavioral Science”. He is the recipient of the Outstanding Contribution Award of IEEE Systems, Man, and Cybernetics Society in 1996, and the Young Scientist Award of China in 1992. He was Secretary General of the 1996 IEEE International Conference on Systems, Man, and Cybernetics in Beijing, Co-chair of the IPC of 1998 International Conference on Systems Science and Systems Engineering, Chair of the First Asian eBiz Workshop in 2001, Co-chair of the Asian eBiz Workshop in 2002 and 2003, and Co-chair of the international conference on Global Supply Chain Management in 2002. Houmin Yan received his B.S. and M.S. from the Department of Automation, Tsinghua University, in 1982 and 1985, respectively, and his Ph.D. from the Faculty of Management, University of Toronto in 1993. From Jan. 1994, he is with the Department of Systems Engineering and Engineering Management, the Chinese University of Hong Kong as an Assistance, Associate and Full Professor. He was a tenured Associate Professor at School of Management, the Univ. of Texas at Dallas. His main research areas are operations management, stochastic models, simulations, and supply chain management. He has published in journals such as Operations Research, Manufacturing and Service Operations Management, Production and Operations Management, Journal of Optimization: Theory and Applications, IIE Transactions and IEEE Transactions. He consults several high-tech companies, such as Motorola, C&K Systems, and Oriental Power, on issues spanning from production planning and scheduling, supply chain management to business process re-engineering. He is a member of INFORMS.